Skip to main content
SpringerLink
Log in

Greedy Algorithm for the Design of Linear-Phase FIR Filters with Sparse Coefficients

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this work, a greedy algorithm for the design of sparse linear-phase finite impulse response filters wherein the coefficients are successively fixed to zero individually is proposed. To meet the filter specifications, the coefficient for which the middle value of its feasible range is closest to zero is selected to be set to zero, whereas all the other unfixed coefficients are free to change. Design examples show that the proposed technique can design FIR filters with higher sparsity than that obtained by existing nonexhaustive algorithms for given specifications. To show the optimality of the algorithm, we design 100 filters, with results showing that the global optimal solution, i.e., the sparsest solution found by exhaustive search, can be achieved in most cases, but with much less computation time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. T. Baran, D. Wei, A.V. Oppenheim, Linear programming algorithms for sparse filter design. IEEE Trans. Signal Process. 58, 1605–1617 (2010)

    Article  MathSciNet  Google Scholar 

  2. A.G. Dempster, M.D. Macleod, Use of minimum-adder multiplier blocks in FIR digital filters. IEEE Trans. Circuits Syst. II 42, 569–577 (1995)

    Article  MATH  Google Scholar 

  3. A. Jiang, H.K. Kwan, Y. Zhu, Peak-error-constrained sparse FIR filter design using iterative SOCP. IEEE Trans. Signal Process. 60, 4035–4044 (2012)

    Article  MathSciNet  Google Scholar 

  4. A. Jiang, H.K. Kwan, WLS design of sparse FIR digital filters. IEEE Trans. Circuits Syst. 60, 125–135 (2013)

    Article  MathSciNet  Google Scholar 

  5. Y.C. Lim, Frequency-response masking approach for the synthesis of sharp linear phase digital filters. IEEE Trans. Circuits Syst. 33, 357–364 (1986)

    Article  Google Scholar 

  6. Y.C. Lim, Y. Lian, The optimum design of one- and two-dimensional FIR filters using the frequency-response masking technique. IEEE Trans. Circuits Syst. II (40), 88–95 (1993)

    Article  MATH  Google Scholar 

  7. W.-S. Lu, T. Hinamoto, Digital filters with sparse coefficients, in Proceedings of the IEEE International Symposium Circuits Systems, Paris, France, (2010), pp. 169–172

  8. Y. Neuvo, D. Cheng-Yu, S.K. Mitra, Interpolated finite impulse response filters. IEEE Trans. Acoust. Speech Signal Process. 32, 563–570 (1984)

    Article  Google Scholar 

  9. W.J. Oh, J.T. Kim, Y.H. Lee, Design of nonuniformly spaced linear-phase FIR filters using mixed integer linear programming. IEEE Trans. Signal Process. 44, 123–126 (1996)

    Article  Google Scholar 

  10. I.-C. Park, H.-J. Kang, Digital filter synthesis based on an algorithm to generate all minimal signed digit representation. IEEE Trans. Comput. Aided Des. 21, 1525–1529 (2002)

    Article  Google Scholar 

  11. R. Paško, P. Schaumont, V. Derudder, D. Duračková, A new algorithm for elimination of common subexpressions. IEEE Trans. Comput. Aided Des. 18, 58–68 (1999)

    Article  Google Scholar 

  12. C. Rusu, B. Dumitrescu, Iterative reweighted \(l_1\) design of sparse FIR filters. Signal Processing 92, 905–911 (2012)

    Article  Google Scholar 

  13. T. Saramaki, Y. Neuvo, S.K. Mitra, Design of computationally efficient interpolated FIR filters. IEEE Trans. Acoust. Speech Signal Process. 35, 70–88 (1984)

    Google Scholar 

  14. D. Shi, Y.J. Yu, Design of linear phase FIR filters with high probability of achieving minimum number of adders. IEEE Trans. Circuits Syst. I 58, 126–136 (2011)

    Article  MathSciNet  Google Scholar 

  15. Y.S. Song, Y.H. Lee, Design of sparse FIR filters based on branch-and-bound algorithm, in Proceedings of the IEEE 40th MidwestSymposium Circuits Systems, Sacramento, CA, (1997), pp. 1445–1448

  16. W.B. Ye, Y.J. Yu, Single-Stage and cascade design of high order multiplierless linear phase FIR filters using genetic algorithm. IEEE Trans. Circuits Syst. I 60, 2987–2997 (2013)

    Article  Google Scholar 

  17. W.B. Ye, Y.J. Yu, Bit-level multiplierless FIR filter optimization incorporating sparse filter technique. IEEE Trans. Circuits Syst. I 61, 3206–3215 (2014)

    Article  Google Scholar 

  18. W.B. Ye, Y.J. Yu, Two-step optimization approach for the design of multiplierless linear-phase FIR filters. IEEE Trans. Circuits Syst. I 62, 1279–1287 (2015)

    Article  MathSciNet  Google Scholar 

  19. W.B. Ye, Y.J. Yu, Single-stage and cascade design of high order multiplierless linear phase FIR filters using genetic algorithm. IEEE Trans. Circuits Syst. I 60, 2987–2997 (2013)

    Article  Google Scholar 

  20. Y.J. Yu, D. Shi, Y.C. Lim, Design of extrapolated impulse response FIR filters with residual compensation in subexpression space. IEEE Trans. Circuits Syst. I 56, 2621–2633 (2009)

    Article  MathSciNet  Google Scholar 

  21. Y.J. Yu, Y.C. Lim, Design of linear phase FIR filters in subexpression space using mixed integer linear programming. IEEE Trans. Circuits Syst. I 54, 2330–2338 (2007)

    Article  MathSciNet  Google Scholar 

  22. H. Zhao, W.B. Ye, Y.J. Yu, Sparse FIR filter design based on genetic algorithm, in Proceedings of the IEEE International Symposium Circuits Systems, Beijing, China, (2013), pp. 97–100

Download references

Author information

Authors and Affiliations

  1. School of Electronic Science and Technology, Shenzhen University, Shenzhen, 518052, China

    Wenbin Ye

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Ya Jun Yu

Authors
  1. Wenbin Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ya Jun Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenbin Ye.

Additional information

This work was partially supported by AcRF TIER 1–RG34/13, NTU.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ye, W., Yu, Y.J. Greedy Algorithm for the Design of Linear-Phase FIR Filters with Sparse Coefficients. Circuits Syst Signal Process 35, 1427–1436 (2016). https://doi.org/10.1007/s00034-015-0122-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0122-5

Keywords

Search

Navigation